Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal Calculator

✖The Longest Section of SD of Unicursal Hexagram is the longest section of the three sections of the short diagonal of the Unicursal hexagram.ⓘ Longest Section of SD of Unicursal Hexagram [d'_{Long(Short Diagonal)}]			+10% -10%
✖The Shortest Section of SD of Unicursal Hexagram is the shortest section of the three sections of the short diagonal of the Unicursal Hexagram.ⓘ Shortest Section of SD of Unicursal Hexagram [d'_{Short(Short Diagonal)}]			+10% -10%
✖A Section of Long Diagonal of Unicursal Hexagram is a particular type of section of the longest diagonal of a Unicursal Hexagram.ⓘ Section of Long Diagonal of Unicursal Hexagram [d'_{Long Diagonal}]			+10% -10%

✖The Area of Unicursal Hexagram is defined as the total quantity of the region enclosed within the Unicursal Hexagram.ⓘ Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal [A]

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Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal

Formula

`"A" = (("d'"_{"Long(Short Diagonal)"}+"d'"_{"Short(Short Diagonal)"})^2*sin(pi/3))+(2*"d'"_{"Short(Short Diagonal)"}*"d'"_{"Long Diagonal"})`

Example

`"154.7077m²"=(("9m"+"3m")^2*sin(pi/3))+(2*"3m"*"5m")`

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Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Unicursal Hexagram = ((Longest Section of SD of Unicursal Hexagram+Shortest Section of SD of Unicursal Hexagram)^2*sin(pi/3))+(2*Shortest Section of SD of Unicursal Hexagram*Section of Long Diagonal of Unicursal Hexagram)
A = ((d'_{Long(Short Diagonal)}+d'_{Short(Short Diagonal)})^2*sin(pi/3))+(2*d'_{Short(Short Diagonal)}*d'_{Long Diagonal})
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Area of Unicursal Hexagram - (Measured in Square Meter) - The Area of Unicursal Hexagram is defined as the total quantity of the region enclosed within the Unicursal Hexagram.
Longest Section of SD of Unicursal Hexagram - (Measured in Meter) - The Longest Section of SD of Unicursal Hexagram is the longest section of the three sections of the short diagonal of the Unicursal hexagram.
Shortest Section of SD of Unicursal Hexagram - (Measured in Meter) - The Shortest Section of SD of Unicursal Hexagram is the shortest section of the three sections of the short diagonal of the Unicursal Hexagram.
Section of Long Diagonal of Unicursal Hexagram - (Measured in Meter) - A Section of Long Diagonal of Unicursal Hexagram is a particular type of section of the longest diagonal of a Unicursal Hexagram.

STEP 1: Convert Input(s) to Base Unit

Longest Section of SD of Unicursal Hexagram: 9 Meter --> 9 Meter No Conversion Required
Shortest Section of SD of Unicursal Hexagram: 3 Meter --> 3 Meter No Conversion Required
Section of Long Diagonal of Unicursal Hexagram: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = ((d'_{Long(Short Diagonal)}+d'_{Short(Short Diagonal)})^2*sin(pi/3))+(2*d'_{Short(Short Diagonal)}*d'_{Long Diagonal}) --> ((9+3)^2*sin(pi/3))+(2*3*5)

Evaluating ... ...

A = 154.707658144959

STEP 3: Convert Result to Output's Unit

154.707658144959 Square Meter --> No Conversion Required

FINAL ANSWER

154.707658144959 ≈ 154.7077 Square Meter <-- Area of Unicursal Hexagram

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Unicursal Hexagram » Area of Unicursal Hexagram » Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal

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< 8 Area of Unicursal Hexagram Calculators

Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal

Go Area of Unicursal Hexagram = ((Longest Section of SD of Unicursal Hexagram+Shortest Section of SD of Unicursal Hexagram)^2*sin(pi/3))+(2*Shortest Section of SD of Unicursal Hexagram*Section of Long Diagonal of Unicursal Hexagram)

Area of Unicursal Hexagram given Perimeter

Go Area of Unicursal Hexagram = 5/6*sqrt(3)*((Perimeter of Unicursal Hexagram)/(2+10/sqrt(3)))^2

Area of Unicursal Hexagram given Short Diagonal

Go Area of Unicursal Hexagram = 5/6*sqrt(3)*(Short Diagonal of Unicursal Hexagram/sqrt(3))^2

Area of Unicursal Hexagram given Longest Section of Short Diagonal

Go Area of Unicursal Hexagram = 20/6*(Longest Section of SD of Unicursal Hexagram)^2/sqrt(3)

Area of Unicursal Hexagram given Shortest Section of Short Diagonal

Go Area of Unicursal Hexagram = 30*(Shortest Section of SD of Unicursal Hexagram)^2/sqrt(3)

Area of Unicursal Hexagram given Medium Section of Short Diagonal

Go Area of Unicursal Hexagram = 15/2*(Medium Section of SD of Unicursal Hexagram)^2/sqrt(3)

Area of Unicursal Hexagram given Long Diagonal

Go Area of Unicursal Hexagram = 5/6*sqrt(3)*(Long Diagonal of Unicursal Hexagram/2)^2

Area of Unicursal Hexagram

Go Area of Unicursal Hexagram = 5/6*sqrt(3)*Edge Length of Unicursal Hexagram^2

Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal Formula

What is Unicursal Hexagram?

A Unicursal Hexagram is a Hexagram or six-pointed star that can be traced or drawn unicursal, in one continuous line rather than by two overlaid triangles. The hexagram can also be depicted inside a circle with the points touching it. It differs from the standard Hexagram as the symbol has equidistant points but the lines are not of the same length.

How to Calculate Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal?

Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal calculator uses Area of Unicursal Hexagram = ((Longest Section of SD of Unicursal Hexagram+Shortest Section of SD of Unicursal Hexagram)^2*sin(pi/3))+(2*Shortest Section of SD of Unicursal Hexagram*Section of Long Diagonal of Unicursal Hexagram) to calculate the Area of Unicursal Hexagram, The Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal formula is defined as the total quantity of the region enclosed within the Unicursal Hexagram, calculated using sections of long diagonal and short diagonal. Area of Unicursal Hexagram is denoted by A symbol.

How to calculate Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal using this online calculator? To use this online calculator for Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal, enter Longest Section of SD of Unicursal Hexagram (d'_{Long(Short Diagonal)}), Shortest Section of SD of Unicursal Hexagram (d'_{Short(Short Diagonal)}) & Section of Long Diagonal of Unicursal Hexagram (d'_{Long Diagonal}) and hit the calculate button. Here is how the Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal calculation can be explained with given input values -> 154.7077 = ((9+3)^2*sin(pi/3))+(2*3*5).

FAQ

What is Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal?

The Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal formula is defined as the total quantity of the region enclosed within the Unicursal Hexagram, calculated using sections of long diagonal and short diagonal and is represented as A = ((d'_{Long(Short Diagonal)}+d'_{Short(Short Diagonal)})^2*sin(pi/3))+(2*d'_{Short(Short Diagonal)}*d'_{Long Diagonal}) or Area of Unicursal Hexagram = ((Longest Section of SD of Unicursal Hexagram+Shortest Section of SD of Unicursal Hexagram)^2*sin(pi/3))+(2*Shortest Section of SD of Unicursal Hexagram*Section of Long Diagonal of Unicursal Hexagram). The Longest Section of SD of Unicursal Hexagram is the longest section of the three sections of the short diagonal of the Unicursal hexagram, The Shortest Section of SD of Unicursal Hexagram is the shortest section of the three sections of the short diagonal of the Unicursal Hexagram & A Section of Long Diagonal of Unicursal Hexagram is a particular type of section of the longest diagonal of a Unicursal Hexagram.

How to calculate Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal?

The Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal formula is defined as the total quantity of the region enclosed within the Unicursal Hexagram, calculated using sections of long diagonal and short diagonal is calculated using Area of Unicursal Hexagram = ((Longest Section of SD of Unicursal Hexagram+Shortest Section of SD of Unicursal Hexagram)^2*sin(pi/3))+(2*Shortest Section of SD of Unicursal Hexagram*Section of Long Diagonal of Unicursal Hexagram). To calculate Area of Unicursal Hexagram given Sections of Long Diagonal and Short Diagonal, you need Longest Section of SD of Unicursal Hexagram (d'_{Long(Short Diagonal)}), Shortest Section of SD of Unicursal Hexagram (d'_{Short(Short Diagonal)}) & Section of Long Diagonal of Unicursal Hexagram (d'_{Long Diagonal}). With our tool, you need to enter the respective value for Longest Section of SD of Unicursal Hexagram, Shortest Section of SD of Unicursal Hexagram & Section of Long Diagonal of Unicursal Hexagram and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Area of Unicursal Hexagram?

In this formula, Area of Unicursal Hexagram uses Longest Section of SD of Unicursal Hexagram, Shortest Section of SD of Unicursal Hexagram & Section of Long Diagonal of Unicursal Hexagram. We can use 7 other way(s) to calculate the same, which is/are as follows -

Area of Unicursal Hexagram = 5/6*sqrt(3)*Edge Length of Unicursal Hexagram^2
Area of Unicursal Hexagram = 5/6*sqrt(3)*(Long Diagonal of Unicursal Hexagram/2)^2
Area of Unicursal Hexagram = 5/6*sqrt(3)*(Short Diagonal of Unicursal Hexagram/sqrt(3))^2
Area of Unicursal Hexagram = 5/6*sqrt(3)*((Perimeter of Unicursal Hexagram)/(2+10/sqrt(3)))^2
Area of Unicursal Hexagram = 20/6*(Longest Section of SD of Unicursal Hexagram)^2/sqrt(3)
Area of Unicursal Hexagram = 30*(Shortest Section of SD of Unicursal Hexagram)^2/sqrt(3)
Area of Unicursal Hexagram = 15/2*(Medium Section of SD of Unicursal Hexagram)^2/sqrt(3)

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